Question

What is the logarithmic function of this graph? also what is the correct base and coefficient of that function when found?

Answer 1

If the function

`y\text{ = }\log _a(x-5)`

Use a point on the graph to find the value of a (the base)

Taking point ( 9, 1 )

`\begin{gathered} y=\log _a(x-5) \\ 1=\text{ }\log _a(9-5) \\ 1=\log _a4 \\ a^1=4\text{ (rule of logarithm)} \\ a^1=4^1 \\ \text{Equating the base} \\ a=\text{ 4} \end{gathered}`

The base of the logarithmic function is 4 and the coefficient of the function is 1